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    Gravitational Potential Energy of a Lake

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    A hydroelectric dam holds back a lake of surface area 3.0*10^6 m^2 that has vertical sides below the water level. The water level in the lake is 150 m above the base of the dam.When the water passes through turbines at the base of the dam, its mechanical energyis converted into electrical energy with 90per cent efficiency.

    1) If gravitationnal potential energy is taken to be zero at the base of the dam, how much energy is stored in the top meter of the water in the lake? The density of water is 1000kg/m^3.

    2) What volume of water must pass through the dam to produce1000kg hours of electrical energy?
    what distance does the level of water in the lake fall when this much water passes through the dam?
    How much energy total is stored in the lake?

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    Solution Preview

    1. E - mg = mgy
    M: mass
    g: 9.8m/s^3
    y: height above base of the dam

    m = Dv
    D: density
    v: volume

    V = Ay
    A: Area of lake

    m = DAy

    E = gDAy^2
    dE = ...

    Solution Summary

    The solution is found by breaking the lake up in to infenetesimal, horizontal layers of thickness dy and integrating to find the total potential energy. Solution includes formulas, full calculations and answer.